Visualizing 2D Flows with Animated Arrow Plots Bruno Jobard1, Nicolas Ray2 and Dmitry Sokolov3 1 LIUPPA laboratory, University of Pau, France, [email protected] 2 ALICE Team, INRIA Nancy Grand-Est, France, [email protected] 3 University of Lorraine, France, [email protected] Figure 1: Ocean currents visualized with a set of dynamic arrows. (Left) The domain is filled with arrows aligned with the flow. The length is proportional to the velocity magnitude. The arrow density is controlled by a custom map to better capture local turbulences. (Right) Close-up showing the arrow trajectories and the morphing of their glyphs. Abstract morphing arrow glyphs to semi-transparent discs. To sub- stantiate our method, we provide results for synthetic and Flow fields are often represented by a set of static ar- real velocity field datasets. rows to illustrate scientific vulgarization, documentary arXiv:1205.5204v1 [cs.GR] 23 May 2012 film, meteorology, etc. This simple schematic represen- tion lets an observer intuitively interpret the main proper- Introduction ties of a flow: its orientation and velocity magnitude. We propose to generate dynamic versions of such representa- Arrow plots are standard static representations for 2D vec- tions for 2D unsteady flow fields. Our algorithm smoothly tor fields. They are intuitive and thus often used to present animates arrows along the flow while controlling their flows mixed with a contextual background image to non- density in the domain over time. Several strategies have expert public. The goal of this work is to provide a simple been combined to lower the unavoidable popping artifacts algorithm that produces clean animated arrow plots for arising when arrows appear and disappear and to achieve presentation purpose. visually pleasing animations. Disturbing arrow rotations This aim greatly differs from the traditional objective in low velocity regions are also handled by continuously as evidenced by the most recent 2D vector field visual- 1 B. Jobard, N. Ray and D. Sokolov Visualizing 2D Flows with Animated Arrow Plots ization techniques, where the efforts have focused on the • an efficient algorithm that controls the density of ar- interactive exploration of the data. For the purpose of ex- rows and manages their life span while maintaining ploration, image-based techniques such as flow textures low popping artifacts, (LIC and its animated extensions) allow for interactive visualization of flow details by using every pixels of the • a rendering algorithm that further reduces popping display device to communicate dense information. How- by both fading arrows in and out, and a morphing ever, flow textures present two major drawbacks in our strategy that handles transitions between high and context: blending them with an additional color map (a low velocity regions, background image or a dynamic field) might greatly dete- • and experimentations on both real and synthetic riorate its details, and such representations are quite sen- flows to evaluate how much the (unavoidable) pop- sitive to the quality of the display device and cannot be ping artifacts can be maintained acceptable for visu- controlled while broadcasting videos or during a public alization purposes. presentation. For the purpose of presentation, a sparse set of moving arrows can easily convey the desired informa- The rest of the paper is organized as follows: after re- tion. The arrows do not deteriorate the background infor- viewing the state of the art, our arrow representation is mation (only occlude it temporary), and is robust to low introduced (Section 1), the arrow generation algorithm is quality display device. provided (Section 2), the capacity to adapt the arrow den- This work proposes a method producing sparse and sity to any density field is explained (Section 3), the ren- smoothly animated representations of a flow with moving dering method is presented (Section 4), and results are arrows (Figure 1). We list below the general properties presented (Section 5) and discussed (Section 6). and constraints such an algorithm should satisfy. Arrow trajectories: to intuitively convey its dynamic nature, the arrow trajectories should follow the flow. Related work Local flow depiction: the arrow shape should depict the local orientation and velocity magnitude of the flow at Most of the recent work on visualizing 2D vector field any time. have targeted the ability for scientists to interactively ex- Uniform domain coverage: the representation should plore their flow datasets. This task is very efficiently provide an uncluttered information of the flow every- achieved with texture-based techniques [9] which offer a where in the domain at any time. dense representation of the fine details of a vector field. Smooth animations: the arrow movement should be They are inexpensive to compute and can produce smooth as smooth as possible to avoid distraction. animations of unsteady flows. However, when combined We propose an algorithm that generates intuitive arrow with a background image, these texture-based represen- plot animations by advecting and bending arrows over tations sometimes fail in displaying both the fine details time while guaranteeing that arrows will not occlude each of the flow and the background (see Section 6.3 and Fig- other and ensuring a complete coverage of the domain. ure 11). In the context of presenting flow behavior in Moreover, the method is able to adapt the density of ar- an animated way to non-expert public, simpler and more rows to arbitrary density field. schematic alternatives are more attractive. However, keeping a uniform coverage of the domain Numerous such geometric based flow visualization with no occlusion involves inserting new arrows to fill the methods were invented over the two last decades [12]. We empty places and removing some arrows in places that focus below on the techniques closely related to visualiza- get too crowded. This necessary insertion and deletion tion of a flow field by animated geometric primitives. of arrows introduce strong popping artifacts when they Vector plots: The simplest vector field visualization appear and disappear, deteriorates the smoothness of the method consists in drawing straight segments originat- animation. Our algorithm has been designed to minimize ing from the nodes of an underlying mesh [2] (Possibly it, both when generating arrows and at rendering time. a Cartesien grid) to indicate the local flow direction and The main contributions in this paper are : possibly its orientation by placing an arrow tip at its other 2 B. Jobard, N. Ray and D. Sokolov Visualizing 2D Flows with Animated Arrow Plots end. Its magnitude might be conveyed by the segment diffusion to better represent the flow. It is even possible length. The main drawback comes from the origin of ar- to represent particules with arrows that are advected by rows being unable to change over time, leading to occlu- the flow [19]. However, arrows will suffer shearing and sions [8] and confusing animations when the vector field could only be used when the support is given by a pathlet is a flow. i.e. advecting a streamlet do not produce a streamlet at the Arrow placement: In flow visualization, clutter and new frame. occlusion problems have been mainly addressed in the Our algorithm better covers the domain and avoids ar- context of streamline placement methods. These algo- row overlaps thanks to more complex creation and dele- rithms apply here since an arrow can be carried by a tion strategies, including backward propagation. Some- small streamline (streamlet) to better depict the local flow. how, it requires relaxing the realtime feature of particle Any of these numerous methods [18, 6, 13, 10] can be tracing. used since they guarantee that no streamlet will be placed within a distance dsep to its neighbours. It is also pos- sible to adapt the streamline density [16]. An animated 1 Moving arrow representation streamline placement has been proposed by Jobard and Lefer [7]. This later work renders the streamlines with During the animation, the arrows are represented with an animated texture that looks like particle trails advected glyphs mapped on rectangular supports. The supports along the streamline. Restricting these particle trails to are warped according to the local flow orientation and be aligned on streamlines makes it impossible to avdect magitude. Each arrow is initiated from a so-called han- them in the flow, and constrains all particles of a stream- dle point and its support is then warped according to a line to be born and die together. Moreover, the lifetime of short streamline integrated backward and forward from streamlines is more sensitive to flow evolution e.g. a flow the handle point (see figure 2). The integration length of with constant rotation in time will create spinning arrows the streamlets is such that their length is proportional to with our algorithm whereas streamlines would have very the local velocity magnitude of the flow. short lifetime. Other methods have been proposed to nicely distribute glyphs. Hiller et al. [5] minimizes Lloyd’s energy to evenly distribute glyph’s positions and other works aim to place a minimal number of glyphs [17, 11] to repre- sent the flow. However, these works do not extend nicely to unsteady flows. An error diffusion approach has been proposed [3] to distribute glyphs in unsteady flows, but it exhibits both high popping and the distribution is not convincing. Figure 2: Arrow Anatomy. An arrow glyph is mapped on Particle tracing: The dynamics of the flow can be re- a rectangular support of a given thickness warped along a vealed by visualizing particles advected in the domain. streamlet integrated from a central handle point. Contrary to arrows, the small size of particle glyphs min- imizes the occlusion problems. Inter particle distances More formally, given a 2D time-dependent vector field has not to be checked and the density is mainly controlled v(x;t) = (vx;vy), a streamline S is a parametric curve S(t) by the seeding strategy.